Radio Broadcast - 1927, May - 61 Pages, 4.9 MB ... - VacuumTubeEra

MAY, 1927 SOME FACTS ABOUT COIL DESIGN 41the usual one. The fact that the of aequivalent in every way toIf we eliminate the unknown current from theThis definition ishigher than for telephony.equations (3) and (4) by substituting the relationselectivitycircuit and the gain go hand in hand is indeed aexpressed in (2), we obtain the following very pleasant one since, if one increases, the otherresults:automatically increases also.'_Eg_ = rrcfl^_ __L l/LTHE EKFICIENCY(5)Ea ~TT~ 2-icfCR R C'"THE expression for the efficiency of an os-or rewriting in the more convenient form, we 1 dilating circuit may be easily obtained byhave, due to inductance:defining the efficiency in the following manner:Eg = Ea(6)ENERGY SUPPLIED PER HALF :CYCLE= EfficiencyThis for convenience may be written as:Eg(7)= EfficiencyENERGY SUPPLIEDor simply:Now, the energy supplied per half cycle is theEg = maximumG Eaenergy stored in the inductance which(8)isgiven by the well known equation:where G is either of the factors given above andalways has a value greater than I. I''unity. That is,Energy = max.the potential applied to the grid of the amplifiertube is always greater than the applied potentialwhere L is the inductance and I max. is the maximumcurrent. Moreover, the energy lost perby a factor "G". The factor "G" is thereforeof the nature of an amplifying factor, and the half cycle is :writer has usually referred to it as the "circuitR lvoltage amplifying factor."i fIt has been suggested that this factor be calledwhere"gain" and since this is a much more R isconvenientterm, we shall now call "G" meanthe equivalent series resistance, I isthe rootthe square current, and f is the frequency.gaindue to the oscillating circuit. Obviously then,Making use of the relation betweenrootthe factor "G," or the gain, should be mademeanassquare current and maximum current,large as possible for any given circuit. To illustratenamely:this idea, suppose we had two oscillatingcircuits, one with a value for "G" of 50 and theother a value of 200. Suppose further, that therewas such an antenna current and such couplingthe efficiency may be written as follows:in both cases that the applied potential was sVof a volt. Then since Kg = LG I max_ R 2 maxIx Ea, the potential~'' 2applied to the grid of the tube (that is the Efficiency 4fJfgeneratedpotential) would be 50 x fa = L I' maxi volt inthe first case and 200 x ^ (4 volts) in the secondObviously then, the coil with a high value and canceling out the common factors, theefficiency reduces to:of "G" would be the best. It may then be said,that in an oscillating circuit, the potential impressedon the grid of an associated tube Efficiency= R IT . 2 x f LI r-ri since G = --dependson the potential applied to the oscillating circuit,and depends equally on a gain factor "G,"which in turn isdependent for its value on theEfficiency = G rc _ G 3.1416circuit constants only.Before considering the application of the above or for per cent, efficiency:results to the determination of the proper coil,it will be valuable to point out the intimate relation,00%between this factor "G" and other char-acteristics of the oscillating circuit. Consider Thus, if the gain is known for any given circuit,the efficiency may readily be computed.first, the relation between the factor "G" andthe selectivity of the circuit. The selectivity, or This equation gives the efficiency of the circuitthe "sharpness of resonance," of an oscillatingin the strict engineering sense and shouldthe circuit is directly proportional to the factor not be construed loosely as a measure of the"G," and if we define selectivity or sharpness of general performance of a coil. The poorest coilsresonance as the ratio of the natural frequency and condensers yield efficiencies of 90 per cent.of the tuned circuit at resonance to the differenceand better while the best coils show efficienciesof the natural frequencies of the circuit of 99 per cent., an apparent increase of but 9when on each side of resonance, such that the per cent. The increase in performance would,oscillating energy on each side or resonance is however, amount to approximately 1300 perjust one half the energy at resonance, then the cent, for the good coil in comparison to the poorselectivity so defined isexactly equal to the factor"G" or:Other things must be considered in radio tele-one.phony besides the intensity of the receivedSelectivity (9) signal. The quality of the received signal is ofgreat importance and if we should increasewhere fr is the natural frequency of the oscillating"G" indefinitely we would soon have a circuitcircuit when in resonance with the incoming that would be so selective that the only fre-wave, f 2 the natural frequency of the tuned circuitquency that would be amplified would be theat a point above resonance, such that the carrier frequency, and the side bands, whichoscillating current is 70.7 per cent, of the current give rise to the speech or music, would be cutat resonance, and fi is the natural frequency of off or, at the least, badly mutilated. There is anthe tuned circuit at a point below resonance, such upper limit to the value of the "gain"if thethat the oscillating current is 70.7 per cent of quality of the speechis to be maintained. Inthe current at resonance.the case of telegraphy, the upper limit is muchCalculations which would be tiresome andout of place in a discussion of this type, showthat if all voice frequencies are to be faithfullyreproduced up to 4000 cycles at a mean wavelengthof 450 meters (666 kc.) the value of thefactor "G" should not materially exceed avalue of 250. This puts a definite upper limit tothe gain or selectivity that can be used in theordinary radio set.Up to this point the discussion relates to thenon-regenerative oscillating circuit as a whole.Now if the condenser used with the inductanceis a good one, having a low resistance, then thelosses of the condenser may, in comparison withthe losses of the coil, be neglected. With thisassumption, which is perfectly legitimate in theaverage case, we may then talk about the "gain"due to the coil, and understand by this, thatthis is the gain that would be obtained if thecoil were used with any condenser of negligibleresistance. These conditions have been met within all experimental data given in this article sincea precision condenser was used which was insulatedwith amber and which had a resistanceof not over 0.2 ohm at 1000 cycles. Thus, at300 meters (1000 kc.), the resistance would beentirely negligible.Considering how the application of the principlesjust discussed are applied to an inductance,we may say that the inductance for any givencircuit should be so chosen that the factor "G,"which, as we have shown, is a measure of theselectivity and the gain, should be as large aspossible, provided it does not greatly exceedthe limiting value for good quality.Returning now to the factors that determinehow large the "gain" will be in any case, equation(5) shows how this factor varies with theinductance, associated capacity, resistance, andthe frequency. It is impossible to examine theequation and say off hand that the ratio of theinductance to the capacity should be very large,as equation (7) would seem to indicate, because,as the inductance of the coil is increased, theresistance increases, perhaps very rapidly, dependingon the physical structure of the coil.On the other hand, if the capacity of the condenseris increased the circuit resistance will decrease,but at a relatively slow rate. It wouldthen appear that in order to determine justwhat combination of inductance and capacityto use or to determine what types of coils arethe best, it will be necessary to make measurementsof this factor "G" and determine experimentallyits values under different circumstances.The factor for the "gain" may be determinedin several different ways. The ratio of the generatedpotential to the applied potential maybe measured directly by means of a vacuumtubevoltmeter, and since by definition thisratio is the "gain," we have a simple methodof getting its value for different coils. The factormay also be determined by use of the definitionfor selectivity as given in equation (9) whichcan be transformed so that known condensersettings may be used instead of frequencies.The values for "G " in this paper were computedfrom the known values of the resistance, inductance,and frequency, since these data werealready available in some cases from previouswork.SOME COILEXPERIMENTSA GREAT many measurements on different'* types of coils have been made during the lastyear in an attempt to obtain sufficient informationto point the way to the design of still bettertypes of coils. Curves showing the "gain" ofvarious representative coils are included in thispaper. In every case but one, the coils were